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Theorem spimev 1939
Description: Distinct-variable version of spime 1916. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spimev.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimev  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1605 . 2  |-  F/ x ph
2 spimev.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spime 1916 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528
This theorem is referenced by:  speiv  1940  axsep  4140  dtru  4201  zfpair  4212  inpc  25277  dominc  25280  rninc  25281
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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